Question

To find the area of a parallelogram use the formula  Areaequalsbtimesh. Use 4one fourth
as the base and 12one half
as the height.

Answer 1

To find the area of a parallelogram using the formula \( \text{Area} = b \times h \), where \( b \) is the base and \( h \) is the height, we first need to convert the mixed numbers into improper fractions or decimals.

The base is given as \( 4 \frac{1}{4} \) and the height as \( 12 \frac{1}{2} \).

1. Convert \( 4 \frac{1}{4} \) to an improper fraction:
\[
4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4}
\]

2. Convert \( 12 \frac{1}{2} \) to an improper fraction:
\[
12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2}
\]

Now we can substitute these values into the area formula:
\[
\text{Area} = b \times h = \left( \frac{17}{4} \right) \times \left( \frac{25}{2} \right)
\]

Calculating the multiplication:
\[
\text{Area} = \frac{17 \times 25}{4 \times 2} = \frac{425}{8}
\]

To convert \( \frac{425}{8} \) to a mixed number, divide 425 by 8:
\[
425 \div 8 = 53 \quad \text{(whole number part)}
\]
The remainder is:
\[
425 - (53 \times 8) = 425 - 424 = 1
\]
So,
\[
\frac{425}{8} = 53 \frac{1}{8}
\]

Thus, the area of the parallelogram is \( \frac{425}{8} \) or \( 53 \frac{1}{8} \) square units.